CN103346798B - A kind of carry out signal acquisition method with the sample frequency lower than nyquist frequency - Google Patents
A kind of carry out signal acquisition method with the sample frequency lower than nyquist frequency Download PDFInfo
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Abstract
The invention discloses a kind of signal acquisition method lower than Nyquist frequency, first against the conversion basic matrix that input signal behavior is suitable, with this conversion basic matrix, signal is carried out rarefaction representation to determine the degree of rarefication k of signal, then calculated the sampling number M of compression sampling by degree of rarefication, then divide M channel respectively to signal with fNYQ/ M samples, and then the sampled value of each channel is integrated, and namely obtains M measured value, and then reconstruction end goes out primary signal by solving-optimizing problem reformulation.The present invention is based on compressive sensing theory, can to sparse signal or the signal of rarefaction representation sampling can be compressed far below the frequency of Nyquist frequency, breach the restriction to sample frequency of the classical Nyquist sampling thheorem, the method is implemented simple simultaneously, reduces the pressure of data acquisition, storage, transmission and process.
Description
Technical field
The present invention relates to one and carry out signal acquisition method with the sample frequency lower than Nyquist (Nyquist) frequency, so that to sparse signal or the signal of rarefaction representation sampling can be compressed far below the sample frequency of Nyquist frequency, and primary signal can be reconstructed.
Background technology
Nyquist sampling thheorem is the basis of modern communication and signal processing, this theorem is pointed out in simulation/digital signal transformation process, when sample frequency is be more than or equal to signal highest frequency 2 times, digital signal after sampling intactly remains the information in primary signal, ensure in general practical application that sample frequency is signal highest frequency 5～10 times.
For broadband signal, owing to itself frequency ratio is higher, if adopting Nyquist sampling thheorem directly signal to be sampled, then the sample frequency needed is just very high, the highest frequency of existing modulus switching device is 1GHz, so being difficult to meet high-frequency requirement.Additionally signal is after analog-digital converter, generally first to store, then data communication and process are carried out again, the processing speed of the storage speed of memorizer, digital signal processor is just required significantly high by high-speed sampling, so broadband signal adopts Nyquist sampling thheorem to carry out sampling and will bring huge pressure to the collection of broadband signal, storage, transmission and process.
Further, since Nyquist sampling thheorem has only developed the minimum prior information of collected signal, i.e. the bandwidth of signal, do not utilize some construction featuress that signal itself has, such as redundancy etc..
Generally handled signal, although signal itself is not sparse, but can rarefaction representation under some conversion base.Compressed sensing is as a new theory, it is simply that utilize this sparse characteristic of signal signal to be sampled far below Nyquist frequency.Compressive sensing theory is pointed out, as long as signal can under certain transform domain rarefaction representation, just with this incoherent observing matrix of conversion basic matrix, high dimensional signal can be projected to a lower dimensional space with one, then pass through solving-optimizing problem from these a small amount of projections, reconstruct original high dimensional signal.
Summary of the invention
(1) to solve the technical problem that
In view of this, it is an object of the invention to provide and a kind of carry out signal acquisition method with the sample frequency lower than nyquist frequency, far below the sample frequency of Nyquist frequency signal sampled and can reconstruct, break through the classical Nyquist sampling thheorem restriction to sample frequency, be reduced to the pressure that the collection of broadband signal, storage, transmission and process bring.
(2) technical scheme
For reaching above-mentioned purpose, the invention provides and a kind of carry out signal acquisition method with the sample frequency lower than nyquist frequency, including: data sending terminal determines the degree of rarefication k of original input signal x, calculate the sampling number M of compression sampling according to this degree of rarefication k, utilize M channel respectively to original input signal x with frequency fNYQ/ M samples, wherein fNYQFor the nyquist frequency of original input signal x, and it is integrated obtaining M measured value y to the sampled value of each channel, then this M measured value y is sent to data receiver；And this M measured value y is carried out orthogonal matching pursuit algorithm and solve by data receiver, by the measured value y the received rarefaction representation reverting to original input signal x, obtain original input signal x again through inverse transformation.
In such scheme, described data sending terminal determines the degree of rarefication k of original input signal x, including: the data sending terminal characters selection and transformation basic matrix according to original input signal x, with this conversion basic matrix, original input signal x is carried out rarefaction representation, then obtain this original input signal x degree of rarefication k under this conversion basic matrix.
In such scheme, described data sending terminal is according in the step of the characters selection and transformation basic matrix of original input signal x, for smooth original input signal, adopts Fourier transformation basic matrix；For the singular signal of single point-like, adopt wavelet transformation basic matrix.It is continually varying sinusoidal signal, cosine signal, exponential signal or sampling pulse that described smooth original input signal includes signal；It is non-continually varying impulse signal, rectangular pulse or spiking that the singular signal of described single point-like includes signal.
In such scheme, described data sending terminal calculates according to degree of rarefication k in the step of sampling number M of compression sampling, and the sampling number M of compression sampling meets following two condition:
A, M >=k ln (N/k), wherein N is the dimension of the original input signal of higher-dimension, and k is original input signal degree of rarefication under correlating transforms base；
B, N=A × M, A is the integer be more than or equal to 1, and namely the dimension of the original input signal of higher-dimension is the integral multiple of the sampling number M of compression sampling.
In such scheme, the sampled value of each channel is integrated obtaining in the step of M measured value y by described data sending terminal, and integration period is A times of each channel sample cycle.
In such scheme, M measured value y is carried out orthogonal matching pursuit algorithm and solves by described data receiver, the measured value y received is reverted to the rarefaction representation of original input signal x, including: according to mathematical operation formula y=Φ x, the measured value y obtained is solved by original input signal x, wherein original input signal x is the vector of N × 1, measured value y is the vector of M × 1, observing matrix Φ is the toeplitz matrix of a M × N, and this matrix is formed by the direction merging of the unit matrix by rows of A=N/M M × M；Known measurements y and observing matrix Φ, it is desirable to solve original input signal x, owing to original input signal x is sparse, it is possible to by solving optimization l1-norm obtains original input signal x, and orthogonal matching pursuit algorithm is exactly a kind of solved, by measured value y and observing matrix Φ, the method obtaining original input signal x by successive ignition.
In such scheme, described data receiver obtains original input signal x by inverse transformation, including: according to the conversion basic matrix selected during to original input signal x rarefaction representation, anti-change is carried out to solving the primary signal rarefaction representation that orthogonal matching pursuit algorithm obtains, if the conversion basic matrix selected during to original input signal x rarefaction representation is Fourier transformation basic matrix, then contravariant is changed to discrete Fourier transform, if the conversion basic matrix selected during to original input signal x rarefaction representation is wavelet transformation basic matrix, then contravariant is changed to wavelet transform.
(3) beneficial effect
Provided by the invention this carry out signal acquisition method with the sample frequency lower than nyquist frequency, based on compressive sensing theory, make full use of the signal sparse characteristic at transform domain, can to sparse signal or the signal of rarefaction representation sampling can be compressed far below the frequency of Nyquist frequency, breach the restriction to sample frequency of the classical Nyquist sampling thheorem, the method is only by low speed sampling and two steps of integration simultaneously, implement simple, reduce the pressure of data acquisition, storage, transmission and process.
Accompanying drawing explanation
In order to illustrate further present disclosure, below in conjunction with accompanying drawing, the present invention is described in detail, wherein:
Fig. 1 is the method flow diagram carrying out signals collecting with the sample frequency lower than nyquist frequency provided by the invention；
Fig. 2 is the schematic diagram carrying out signals collecting according to the embodiment of the present invention；
Fig. 3 is the schematic diagram carrying out signal reconstruction according to the embodiment of the present invention；
Fig. 4 is that wherein the left side is primary signal figure, and the right is the sparse table diagram after Fourier transformation according to embodiment of the present invention 50Hz, 100Hz, the sinusoidal signal of 150Hz and 200Hz and frequency domain representation thereof；
Fig. 5 is the sampling according to embodiment of the present invention signal and quality reconstruction figure, and (a) is primary signal, the error of (b) sampled value, (c) reconstruction signal, (d) reconstruction signal and primary signal.
Detailed description of the invention
For making the object, technical solutions and advantages of the present invention clearly understand, below in conjunction with specific embodiment, and with reference to accompanying drawing, the present invention is described in more detail.
As shown in Figure 1, Fig. 1 is the method flow diagram carrying out signals collecting with the sample frequency lower than nyquist frequency provided by the invention, the method, on compressive sensing theory basis, with the collection realizing signal of the frequency high probability far below Nyquist frequency, comprises the following steps:
Data sending terminal determines the degree of rarefication k of original input signal x, calculates the sampling number M of compression sampling according to this degree of rarefication k, utilize M channel respectively to original input signal x with frequency fNYQ/ M samples, wherein fNYQFor the nyquist frequency of original input signal x, and it is integrated obtaining M measured value y to the sampled value of each channel, then this M measured value y is sent to data receiver；And
This M measured value y is carried out orthogonal matching pursuit algorithm and solves by data receiver, by the measured value y the received rarefaction representation reverting to original input signal x, obtains original input signal x again through inverse transformation.
Wherein, described data sending terminal determines the degree of rarefication k of original input signal x, including: the data sending terminal characters selection and transformation basic matrix according to original input signal x, with this conversion basic matrix, original input signal x is carried out rarefaction representation, then obtain this original input signal x degree of rarefication k under this conversion basic matrix.Described data sending terminal is according in the step of the characters selection and transformation basic matrix of original input signal x, for smooth original input signal, adopts Fourier transformation basic matrix；For the singular signal of single point-like, adopt wavelet transformation basic matrix.Described smooth original input signal includes the continually varying signals such as sinusoidal signal, cosine signal, exponential signal or sampling pulse；The singular signal of described single point-like includes the signal of the discontinuous changes such as impulse signal, rectangular pulse or spiking.
Described data sending terminal calculates in the step of sampling number M of compression sampling according to degree of rarefication k, the sampling number M of compression sampling meets following two condition: a, M >=k ln (N/k), wherein N is the dimension of the original input signal of higher-dimension, and k is original input signal degree of rarefication under correlating transforms base；B, N=A × M, A is the integer be more than or equal to 1, and namely the dimension of the original input signal of higher-dimension is the integral multiple of the sampling number M of compression sampling.The sampled value of each channel is integrated obtaining in the step of M measured value y by described data sending terminal, and integration period is A times of each channel sample cycle.
M measured value y is carried out orthogonal matching pursuit algorithm and solves by described data receiver, the measured value y received is reverted to the rarefaction representation of original input signal x, it is according to mathematic(al) representation y=Φ x, the process of original input signal x is solved by successive ignition by measured value y and observing matrix Φ, including: according to mathematical operation formula y=Φ x, the measured value y obtained is solved by original input signal x, wherein original input signal x is the vector of N × 1, measured value y is the vector of M × 1, observing matrix Φ is the toeplitz matrix of a M × N, this matrix is formed by the direction merging of the unit matrix by rows of A=N/M M × M；Known measurements y and observing matrix Φ, it is desirable to solve original input signal x, owing to original input signal x is sparse, it is possible to by solving optimization l1-norm obtains original input signal x, and orthogonal matching pursuit algorithm is exactly a kind of solved, by measured value y and observing matrix Φ, the method obtaining original input signal x by successive ignition.
Described data receiver obtains original input signal x by inverse transformation, including: according to the conversion basic matrix selected during to original input signal x rarefaction representation, anti-change is carried out to solving the primary signal rarefaction representation that orthogonal matching pursuit algorithm obtains, if the conversion basic matrix selected during to original input signal x rarefaction representation is Fourier transformation basic matrix, then contravariant is changed to discrete Fourier transform, if the conversion basic matrix selected during to original input signal x rarefaction representation is wavelet transformation basic matrix, then contravariant is changed to wavelet transform.
Based on the method flow diagram carrying out signals collecting with the sample frequency lower than nyquist frequency provided by the invention shown in Fig. 1, Fig. 2 to Fig. 5 for frequency be 50Hz, the sinusoidal signal of 100Hz, 150Hz and 200Hz (signal length is for N=256), the present invention is described in more detail.Wherein, Fig. 2 is the schematic diagram carrying out signals collecting according to the embodiment of the present invention, and Fig. 3 is the schematic diagram carrying out signal reconstruction according to the embodiment of the present invention, is specifically divided into three below step:
Step 1: original input signal x is carried out rarefaction representation by data sending terminal；
Owing to being sinusoidal signal, so data sending terminal adopts Fourier transformation basic matrix that original input signal is carried out rarefaction representation, as shown in Figure 4, the left side is original input signal figure, the right is the sparse table diagram after signal Fourier transformation, it is found that this original input signal only has 8 nonzero values, other values are all zero, i.e. the degree of rarefication k=8 of this signal；
Step 2: data sending terminal to original input signal x at fNYQSample under the sample frequency of/M；
First determining the value of the sampling number M of compression sampling, owing to M to meet two conditions: (a) M >=k ln (N/k), wherein N is the dimension of original high dimensional signal, and k is signal degree of rarefication under correlating transforms base；B () N=A × M, A is the integer be more than or equal to 1, so taking M=32, A=8 here；Then divide 32 channels respectively to original input signal x at fNYQ/32(fNYQ=400Hz) sample under sample frequency, the sampled value that each channel obtains is 8, and 8 sampled values of each channel are integrated, integration period is A times of each channel sample cycle, so can be obtained by 32 measured value y, directly these 32 measured value y are sent to data receiver；As shown in Fig. 5 (a), for primary signal figure；As shown in Fig. 5 (b), for 32 sampled values obtained.
Step 3: data receiver reconstructs original input signal x；
Data receiver utilizes orthogonal matching pursuit algorithm, the low-dimensional data (i.e. measured value y) received is reconstructed into original high dimensional data, the measured value y obtained after step 1 and 2 is equivalent to following mathematical operation formula y=Φ x, the measured value y obtained is solved by original input signal x, wherein original input signal x is the vector of N × 1, measured value y is the vector of M × 1, observing matrix Φ is the toeplitz matrix of a M × N, and this matrix is formed by the direction merging of the unit matrix by rows of A=N/M M × M；Known measurements y and observing matrix Φ, it is desirable to solve original input signal x, owing to original input signal x is sparse, it is possible to by solving optimization l1-norm obtains original input signal x, and orthogonal matching pursuit algorithm is exactly a kind of solved, by measured value y and observing matrix Φ, the method obtaining original input signal x by successive ignition.
(c) such as Fig. 5 show the signal reconstructed, and error is 10-14The order of magnitude, very little, Fig. 5 (d) show the difference of signal and the primary signal reconstructed, and magnitude is 10-13, it is seen that the method can realize the compression sampling of signal with the frequency far below Nyquist frequency, and extraordinary can be recovered original high dimensional signal by few sampled value.
Particular embodiments described above; the purpose of the present invention, technical scheme and beneficial effect have been further described; it is it should be understood that; the foregoing is only specific embodiments of the invention; it is not limited to the present invention; all within the spirit and principles in the present invention, any amendment of making, equivalent replacement, improvement etc., should be included within protection scope of the present invention.
Claims (6)
1. one kind carries out signal acquisition method with the sample frequency lower than nyquist frequency, it is characterised in that including:
Data sending terminal determines the degree of rarefication k of original input signal x, calculates the sampling number M of compression sampling according to this degree of rarefication k, utilize M channel respectively to original input signal x with frequency fNYQ/ M samples, wherein fNYQFor the nyquist frequency of original input signal x, and it is integrated obtaining M measured value y to the sampled value of each channel, then this M measured value y is sent to data receiver；And
This M measured value y is carried out orthogonal matching pursuit algorithm and solves by data receiver, by the measured value y the received rarefaction representation reverting to original input signal x, obtains original input signal x again through inverse transformation；
Wherein, described data sending terminal calculates in the step of sampling number M of compression sampling according to degree of rarefication k, the sampling number M of compression sampling meets following two condition: a, M >=k ln (N/k), wherein N is the dimension of the original input signal of higher-dimension, and k is original input signal degree of rarefication under correlating transforms base；B, N=A × M, A is the integer be more than or equal to 1, and namely the dimension of the original input signal of higher-dimension is the integral multiple of the sampling number M of compression sampling；
M measured value y is carried out orthogonal matching pursuit algorithm and solves by described data receiver, the measured value y received is reverted to the rarefaction representation of original input signal x, including: according to mathematical operation formula y=Φ x, the measured value y obtained is solved by original input signal x, wherein original input signal x is the vector of N × 1, measured value y is the vector of M × 1, and observing matrix Φ is the toeplitz matrix of a M × N, and this matrix is formed by the direction merging of the unit matrix by rows of A=N/M M × M；Known measurements y and observing matrix Φ, it is desirable to solve original input signal x, owing to original input signal x is sparse, it is possible to by solving optimization l1-norm obtains original input signal x, and orthogonal matching pursuit algorithm is exactly a kind of solved, by measured value y and observing matrix Φ, the method obtaining original input signal x by successive ignition.
2. according to claim 1 carry out signal acquisition method with the sample frequency lower than nyquist frequency, it is characterised in that described data sending terminal determines the degree of rarefication k of original input signal x, including:
The data sending terminal characters selection and transformation basic matrix according to original input signal x, carries out rarefaction representation with this conversion basic matrix to original input signal x, then obtains this original input signal x degree of rarefication k under this conversion basic matrix.
3. according to claim 2 carry out signal acquisition method with the sample frequency lower than nyquist frequency, it is characterized in that, described data sending terminal is according in the step of the characters selection and transformation basic matrix of original input signal x, for smooth original input signal, adopt Fourier transformation basic matrix；For the singular signal of single point-like, adopt wavelet transformation basic matrix.
4. according to claim 3 carry out signal acquisition method with the sample frequency lower than nyquist frequency, it is characterised in that it is continually varying sinusoidal signal, cosine signal, exponential signal or sampling pulse that described smooth original input signal includes signal；It is non-continually varying impulse signal, rectangular pulse or spiking that the singular signal of described single point-like includes signal.
5. according to claim 1 carry out signal acquisition method with the sample frequency lower than nyquist frequency, it is characterized in that, the sampled value of each channel is integrated obtaining in the step of M measured value y by described data sending terminal, and integration period is A times of each channel sample cycle.
6. according to claim 1 carry out signal acquisition method with the sample frequency lower than nyquist frequency, it is characterised in that described data receiver obtains original input signal x by inverse transformation, including:
According to the conversion basic matrix selected during to original input signal x rarefaction representation, anti-change is carried out to solving the primary signal rarefaction representation that orthogonal matching pursuit algorithm obtains, if the conversion basic matrix selected during to original input signal x rarefaction representation is Fourier transformation basic matrix, then contravariant is changed to discrete Fourier transform, if the conversion basic matrix selected during to original input signal x rarefaction representation is wavelet transformation basic matrix, then contravariant is changed to wavelet transform.
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| WO2014194485A1 (en) * | 2013-06-05 | 2014-12-11 | 中国科学院微电子研究所 | Method for collecting signal with sampling frequency lower than nyquist frequency |
| WO2015131396A1 (en) * | 2014-03-07 | 2015-09-11 | 中国科学院微电子研究所 | One-dimensional signal random sampling method based on compressed sensing |
| CN103795422B (en) * | 2014-03-07 | 2017-07-14 | 中国科学院微电子研究所 | A kind of one-dimensional signal stochastical sampling method based on compressed sensing |
| WO2015139260A1 (en) * | 2014-03-20 | 2015-09-24 | 华为技术有限公司 | Compressive sensing-based signal processing method and device |
| CN105072446B (en) * | 2015-07-27 | 2018-05-04 | 福州大学 | The compression sampling and restructing algorithm of a kind of coloured image |
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| CN108663606A (en) * | 2018-05-17 | 2018-10-16 | 国网辽宁省电力有限公司电力科学研究院 | A kind of method and system that local discharge signal is acquired with low sample frequency |
| CN109100700B (en) * | 2018-10-26 | 2020-12-01 | 深圳大学 | Single sampling radar signal processing system and method |
| CN111010191B (en) * | 2019-12-12 | 2023-11-07 | 国家电网有限公司大数据中心 | Data acquisition method, system, equipment and storage medium |
| CN111490794B (en) * | 2020-04-17 | 2021-12-10 | 山东大学 | Method for improving frequency response of phase-sensitive OTDR system |
| CN112699185A (en) * | 2021-01-18 | 2021-04-23 | 上海对外经贸大学 | Block chain compressed sensing storage method based on discrete transformation and sparse sampling |
| CN113271477B (en) * | 2021-05-17 | 2022-07-08 | 中国工商银行股份有限公司 | Video data transmission method, device and system |
| CN114070326B (en) * | 2021-11-09 | 2022-10-11 | 中北大学 | Reconstruction method for acquiring ultrahigh frequency signal by equivalent time sampling |
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